To compare the efficacy of the proposed algorithms and the separation quality,
we conducted an audio BSS experiment with simulated mixtures of
a directional target speech and diffuse babble noise.
We compared three methods:
FastMNMF [1]},
FastMNMF initialized by ILRMA (ILRMA+FastMNMF),
and rank-constrained SCM estimation initialized by ILRMA [2]}.
For rank-constrained SCM estimation, we compared three update algorithms, namely,
the naive update rule (Naive) and the proposed update rules
with the first and second accelerations (Proposed 1st-stage accel. and Proposed 2nd-stage accel., respectively).
In ILRMA, the observation \(\mathbf {x}_{ij}\)  was preprocessed via a sphering transformation using principal component analysis.
For ILRMA and FastMNMF, all the NMF variables were initialized by nonnegative random values.
The demixing matrix \(\mathbf {\mathrm {W}}_{i}\)  in ILRMA and the spatial covariance matrix in FastMNMF were initialized by the identity matrix.
For ILRMA+FastMNMF, the NMF variables were initialized using the estimates of ILRMA.
Also, the spatial covariance matrix was initialized using \(\mathbf {a}_{i,n}\mathbf {a}_{i,n}^{\mathsf {H}}+\varepsilon \sum _{n^{\prime }\ne n}\mathbf {a}_{i,n^{\prime }}\mathbf {a}_{i,n^{\prime }}^{\mathsf {H}}\)  for ILRMA+FastMNMF, where \(\mathbf {a}_{i,n}\)  was estimated by ILRMA and \(\varepsilon \)  was set to \(10^{-5}\) .
These methods were implemented in MATLAB (R2019a),
and the computation was performed on an Intel Core i9-7900X (3.30 GHz, 10 cores) CPU.
The dry sources of the directional target speech and diffuse babble noise
were obtained from the JNAS speech corpus [3]}.
They were convoluted with the impulse responses shown in Fig. REF  to simulate a mixture of 8.7 s length.
The target source was located 30\(^{\circ }\)  clockwise from the normal to a microphone array,
the 19 loudspeakers used to simulate diffuse noise were arranged at intervals of 10\(^{\circ }\) ,
the size of the recording room for these impulse responses was 3.9 m \(\times \)  3.9 m,
and its reverberation time was about 200 ms.
Note that the diffuse babble noise was produced by convoluting 19 independent speeches with each impulse response.
The speech-to-noise ratio was set to 0 dB.
The other conditions are shown in Table REF .
